CN102622517A - Method for identifying hydrologic time series cycle - Google Patents
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Abstract
The invention discloses a method for identifying a hydrologic time series cycle. The method comprises the steps as follows: firstly, checking the reliability of the analyzed series, reasonably selecting a curve fitting method, a boundary point processing method and a termination condition, decomposing the series by using an ensemble empirical mode decomposition (EEMD) method, and identifying maximum intrinsic mode functions (MIMFs) in all the intrinsic mode functions (IMFs); secondly, for each MIMFs, identifying the cycle by using a maximum entropy spectrum analysis (MESA) method; and lastly, integrating the cycle identification results of the MIMFs so as to obtain the cycle of the analyzed series. The method is based on the EEMD method, so that the method is suitable for the analysis of the hydrologic time series with non linearity and non stability.
Description
Technical field
The present invention relates to the hydrological science technical field, specifically is a kind of method of discerning the Hydrological Time Series cycle.
Background technology
The Hydrological Time Series analysis has great importance to the understanding hydrologic process
[1,2]During hydrological sequence analysis, the identification of periodic component and extraction are crucial contents, but the periodic component of accurately discerning hydrology sequence is the comparatively work of difficulty.Tradition cycle recognition methods mainly is based on correlation analysis or Fourier conversion (Fourier transform; FT) spectral analysis method; Therefore there are a lot of shortcomings in they; For example, the non-true hypothesis when low resolution, the subjectivity when selecting high-order coefficient of autocorrelation or window function, extension sequence etc.
[3]Pseudoperiodicity usually appears in the sequence estimation power spectrum that is obtained by classic method, and some true cycles can not show sometimes.In order to overcome the defective of tradition cycle recognition methods, some improved cycle recognition methodss are constantly proposed and are incorporated in the hydrological sequence analysis.At present, using the most extensive and ripe method is the maximum entropy spectrum analysis method (MESA) that Burg proposes
[4]This method is based on principle of maximum entropy (POME)
[5], and be superior to traditional spectral analysis method.But when this method was applied to hydrological sequence analysis, particularly hydrology sequence contained the much noise composition, or when having a plurality of spectrum peak, the analysis result of MESA method need be treated cautiously.
Occurring in nature, actual measurement Hydrological Time Series usually receive many at random with the interference and the influence of uncertain factor, therefore always contain noise contribution in various degree.In fact, noise contribution can produce many complicacies and irregular spectral fluctuations, makes that real frequency spectrum is polluted; Be submerged in these complicacies and the irregular spectral fluctuations; Spectrogram is smooth inadequately on the whole, and resolution is not high, shows some pseudoperiodicities sometimes.Therefore, directly use the MESA method hydrology sequence is carried out when identification in cycle, the superiority of this method can not embody well.For overcoming the influence of noise contribution to Hydrological Time Series cycle recognition result, people such as Sang Yanfang proposed a chief series cycle recognition methods (main series spectral analysis, MSSA)
[6], and the instance analysis result verification validity of this method.
Yet except containing noise contribution, the actual measurement Hydrological Time Series also shows dimensional variation characteristic of many time, and promptly Hydrological Time Series usually is not that single one-tenth is grouped into by multicomponent.If can at first separate the heterogeneity and then the cycle of the carrying out identification of hydrology sequence, also can improve the precision of analysis result.In the sequence decomposition method that uses at present, wavelet-decomposing method is the method for using always, but the result receives the influence of many factors, for example wavelet function selection and decomposition level selection etc.
[7]In addition, wavelet-decomposing method generally is that binary orthogonal is decomposed, and these are under many actual conditions and do not meet physical process.Than wavelet-decomposing method, (empirical mode decomposition EMD) is another more excellent method relatively to empirical mode decomposition method
[8]When using the EMD method, any sequence all can resolve into a series of intrinsic mode functions (intrinsic mode functions, IMFs).Because the EMD method is based on the localized variation characteristic of sequence self, so this method has adaptability and validity preferably.
Summary of the invention
Technical matters to be solved by this invention provides a kind of being more suitable in the new method of Hydrological Time Series being carried out cycle identification.
A kind of method of discerning the Hydrological Time Series cycle is characterized in that may further comprise the steps:
1) reliability of the inspection Hydrological Time Series of analyzing at first, pass through selection rational curve-fitting method, frontier point disposal route and end condition then after, confirm concrete population mean empirical mode decomposition method (EEMD);
2) use determined EEMD method and sequence is decomposed sequence
X (t)Decomposition result be designated as:
Wherein,
NThe number of the intrinsic mode function (IMFs) that expression identifies,
C i Expression the
iIndividual IMF,
R N Be last residual components, general corresponding the trend of sequence;
3) utilize the energy dispersal function of white noise, identify the determinacy intrinsic mode function (MIMFs) among all IMFs;
4), use MESA method recognition cycle for each MIMFs;
5) the cycle recognition result of last comprehensive each MIMFs obtains cycle of the Hydrological Time Series of analyzing.
Said EEMD method is carried out step of decomposition 2 to sequence) process is:
(1) initialization:
i=1, and definition
r 0 =
X (t)
(2) for
r 0 , discern all Local Extremum, comprise maximum value and minimal value, utilize cubic spline curve approximating method respectively match local maximum point and minimum point then, and as on cover line and under cover line;
(3) contrast and find the solution the average curve that covers line up and down
m (j=1)
(4) through finding the solution sequence
r 0 With
m (j=1) Difference, obtain first sequence
h (j=1)
(5) will
h (j=1) As
r 0 Repeating step (2)-(4) then, constantly promptly
j=
j+ 1 is satisfying the requirement that meets under the certain criterion about horizontal ordinate symmetry until covering line up and down, last
h (j) The result is designated as
C i
(6) definition again
r 0 =
X (t)-
C i And
i=
i+ 1, repeating step (1)-(5) then, when
i=
NAnd residual components
R N Become a monotonic quantity, when only comprising inner extreme point and can not discern any IMF again, " screening " process finishes.
The process of said step 4) is:
Order
XExpression waits to estimate the hydrology sequence of frequency spectrum, and the relational expression of hydrology sequence spectrum and entropy is:
(1)
Wherein,
f N Expression Nyquist frequency,
S (f)The expression frequency
fThe spectrum value at place,
E d Then represent entropy density.
For the hydrology sequence of appointment, formula (1) right-hand member first is a constant, and solution procedure only need guarantee that the integral maximization of second portion gets final product, so formula (1) can be reduced to:
Maximization:
(2)
Constraints:
? (3)
Wherein,
mThe maximum time lag of expression appointment,
i=(1)
1/2,
r x (k)The expression sequence
X kThe rank coefficient of autocorrelation;
Likewise, if wait to estimate frequency spectrum only with known exponent number on autocorrelation performance relevant, must satisfy the differentiate result of formula (4):
Following formula shows function
1/S (f)The Fourier transformation results in time lag
K=mThe place is blocked, and can obtain formula (5) then:
Maximum time lag or filter length do
mThe time, can obtain formula (6) through finding the solution entropy maximization:
In the formula,
P (m+1)Expression is to the energy value of back prediction error, γ
x (j)The filter coefficient that expression is used to forecast,
γ x (j)With
P (m+1)Then estimate to find the solution frequency spectrum through recursive algorithm
S (f)Estimate to obtain by formula (7):
The present invention unites use with EEMD and MESA method, proposes a kind of Hydrological Time Series cycle recognition methods-EEMD-MESA.Therefore this method is applicable to analyze to have non-linear and Hydrological Time Series non-stationary property based on the EEMD method.
Description of drawings
Fig. 1. 54 years annual flow sequences (a) of station, Lijin actual measurement, and EEMD decomposition result (b),
Fig. 2. 54 years annual flow sequence determinacy composition recognition results (a) of station, Lijin actual measurement and cycle recognition result (b),
Fig. 3. FFT, MESA and the MSSA cycle recognition result of 54 years annual flow sequences of station, Lijin actual measurement.
Embodiment
Detailed process of the present invention:
1. EMD decomposition method
Use the EMD method that the heterogeneity of hydrology sequence is separated the back result and be called intrinsic mode function (IMF).Each intrinsic mode function must satisfy two conditions
[8]: (1) extreme value number and zero crossing number must equate or differ from one at the most; (2) location point any time is by covering line and must be symmetrical about transverse axis by the following line that covers of local minizing point's decision in the local maximum point decision.Definition according to IMF can be found out, the fluctuation model that on behalf of sequence, each IMF comprise, and also each IMF is the first-order stationary sequence.Through sequence being resolved into a series of IMFs, can disclose and be familiar with the complicated variation characteristic of sequence under the different time yardstick; In addition, utilize methods such as FT and MESA that the cycle of IFMs is discerned, also can disclose the periodic component of former sequence.
Suppose that time series is made up of IMFs, can utilize EMD that sequence is decomposed.The EMD method is to utilize the sequence extreme point to carry out the process of " screening ".For time series
X (t), decomposable process is described below
[8,9]:
(7) initialization:
i=1, and definition
r 0 =
X (t)
(8) for
r 0 , discern all Local Extremum (comprising maximum value and minimal value), utilize suitable curve-fitting method match local maximum point and minimum point respectively then, and as on cover line and under cover line.Actual cubic spline curve approximating method commonly used;
(9) contrast and find the solution the average curve that covers line up and down
m (j=1)
(10) through finding the solution sequence
r 0 With
m (j=1) Difference, obtain first sequence
h (j=1)
(11) will
h (j=1) As
r 0 Repeating step (2)-(4) then, constantly promptly
j=
j+ 1 is satisfying the requirement that meets under the certain criterion about horizontal ordinate symmetry until covering line up and down.Last
h (j) The result is designated as
C i
(12) definition again
r 0 =
X (t)-
C i And
i=
i+ 1, repeating step (1)-(5) then.When
i=
NAnd residual components
R N Become a monotonic quantity, when only comprising inner extreme point and can not discern any IMF again, " screening " process finishes.
Such as above-mentioned step description because the EMD method only relies on the Local Extremum of sequence self to decompose, therefore have good applicability, can be used for analyzing any time series with complex nonlinear and non-stationary property.For the sequence decomposition result of EMD method, the IMF that decomposites at first has highest frequency, corresponding minimum time yardstick.Along with " screening " process is carried out, the frequency that the IMF that decomposites is corresponding reduces gradually; Decomposite at last
R N Corresponding frequency is minimum, and generally is the trend of institute's analytical sequence.
In the actual sequence EMD analytic process, the influence of many keys and difficult point factor be can receive, suitable curve-fitting method, boundary effect and end condition etc. for example selected
[8]For improving EMD methods analyst result's reliability, this paper uses improving one's methods of EMD---and the EEMD method is carried out the sequence decomposition, and its basic ideas are constantly to analyze superimposed noise sequence afterwards, average as end product then
[9]
In addition, the sequence decomposition result of EEMD method often comprises the false IMFs that some lack the actual physics meaning.Therefore for obtaining rationally sequence decomposition result reliably, we need at first identify real IMFs.The method of using Wu and Huang (2004) to propose here,
[10]The characteristic that this method shows after EMD decomposes according to white noise through the energy dispersal function of contrast white noise and the EMD result of Hydrological Time Series, can identify the determinacy composition exactly, also can quantitatively estimate uncertainty.
2. entropy spectral analysis method (MESA)
Order
XExpression waits to estimate the hydrology sequence of frequency spectrum, when application MESA method is analyzed, mainly carries out cycle identification based on the relation of sequence spectrum and entropy
[6]:
Wherein,
f N Expression Nyquist frequency,
S (f)The expression frequency
fThe spectrum value at place,
E d Then represent entropy density.
The basic ideas of MESA method are under the constraint condition that the spectrum value of desiring to find the solution and auto-correlation estimated result are consistent, and realize
E d The maximization of entropy function
[11]Because for the hydrology sequence of appointment, formula (1) right-hand member first is a constant, and solution procedure only need guarantee that the integral maximization of second portion gets final product.Therefore formula (1) can be reduced to:
Maximization:
(2)
Constraints:
? (3)
Wherein,
mThe maximum time lag of expression appointment,
i=(1)
1/2 r x (k)The expression sequence
X kThe rank coefficient of autocorrelation.
Likewise, if wait to estimate frequency spectrum only with known exponent number on autocorrelation performance relevant, must satisfy the differentiate result of formula (4):
Following formula shows function
1/S (f)The Fourier transformation results in time lag
K=mThe place is blocked, and can obtain formula (5) then:
Maximum time lag or filter length do
mThe time, can obtain formula (6) through finding the solution entropy maximization:
In the formula,
P (m+1)Expression is to the energy value of back prediction error, γ
x (j)The filter coefficient that expression is used to forecast.
γ x (j)With
P (m+1)Can estimate to find the solution through recursive algorithm.Many selective filter length are arranged at present
mMethod, for example, last prediction error criterion (final predict error criterion; FPE), and Akaike's Information Criterion (Akaike information criterion, AIC); Bayesian information criterion (Bayesian information criterion; BIC), PLS criterion (partial least square criterion, PLS) etc.).Frequency spectrum
S (f)Estimate to obtain by formula (7):
3. the cycle is discerned new method
Use EEMD and MESA method through uniting, proposed one-period identification new method.The EEMD method is used to discern and the determinacy composition that separates Hydrological Time Series, and the MESA method is used to discern the cycle of each determinacy composition.At last, the periodic component of the Hydrological Time Series of analyzing can be by accurate identification.The concrete analysis process is following:
(1) at first checks the reliability of institute's analytical sequence.Through selecting rational curve-fitting method, frontier point disposal route and end condition, confirm concrete EEMD method;
(2) using determined EEMD method decomposes sequence.Sequence
X (t)Decomposition result be designated as:
Wherein,
NThe number of the IMFs that expression identifies,
C i Expression the
iIndividual IMF,
R N It is last residual components;
(3) utilize the energy dispersal function of white noise, identify the determinacy intrinsic mode function (MIMFs) among all IMFs;
(4), use MESA method recognition cycle for each MIMFs;
(5) the cycle recognition result of last comprehensive each MIMFs obtains cycle of institute's analytical sequence.
4. sample calculation analysis
Institute's extracting method is applied to station, Lijin, the Yellow River actual measurement 54 years (1950 ~ 2003) annual flow sequence (Fig. 1 (a)) to be analyzed.Show through a plurality of method synthesis results of study that at present this sequence mainly contained for 3,7,11 and 18 annual periods
[6]The EEMD analysis result of this actual measurement runoff sequence is shown in Fig. 1 (b).Wherein, in the concrete EEMD decomposable process, use the cubic spline difference approach to carry out curve fitting, use the point symmetry method to handle boundary effect, and the Cauchy method of using document [9] is as the end condition of screening etc.
Then, the EEMD decomposition result of this runoff sequence is carried out the identification of determinacy composition, the result is shown in Fig. 2 (a).Can find out that the energy value of the 2nd, 3 and 4 the isolated IMF (being designated as IMF2, IMF3 and IMF4 respectively) of this runoff sequence is positioned on 95% fiducial interval, therefore think that they mainly are made up of the determinacy composition.Afterwards, use the MESA method these 3 IMF are carried out cycle identification, the result sees Fig. 2 (b).In addition,, use FFT, MESA and MSSA method equally this runoff sequence is analyzed, the results are shown in shown in Figure 3 for ease of comparative analysis as a result.
The cycle recognition result of analysis-by-synthesis Fig. 2 and Fig. 3 can be found out: (1) based on Fig. 2 result, the determinacy composition of this runoff sequence can be by accurate identification.This sequence comprises three determinacy compositions, and residual components corresponding the trend of sequence; (2) the IMF2 composition showed for 3 annual periods, and the IMF3 composition has shown 7 years and 11 annual periods, and the IMF4 sequence showed for 18 annual periods.Therefore think that based on the EEMD method four cycles of this runoff sequence all can be by accurate identification; (3) for the cycle recognition result of conventional method, the FFT spectrogram shows irregular fluctuation, but does not show obvious periodic; The MESA method can not discern for 11 annual periods, and the MSSA method can identify four periodic quantities of this sequence, but can not clearly be identified for 3 annual periods; (4) four methods of contrast, EEMD-MESA is superior to other three methods, and the analysis result of FFT method is the poorest.
List of references
[1]?Yevjevich,?V.?Stochastic?Process?in?Hydrology.?Water?Resources?Publications,?Colorado,?1972.
[2] fourth is brilliant, Deng Yuren. statistical hydrology [M]. and Chengdu: publishing house of Chengdu Univ. of Science & Technology, 1988.
[3]?Padmanabhan,?G.,?A.R.?Rao.?Maximum?entropy?spectral?analysis?of?hydrologic?data.?Water?Resour.?Res.?1988,?24,?1519-1533.
[4]?Burg,?J.P.A.?A?new?analysis?technique?for?time?series?data.?Paper?presented?at?the?NATO?Advanced?Study?Institute?on?Signal?Processing?with?Emphasis?on?Underwater?Acoustics.?Enschede.?The?Netherlands,?12-12,?Aug.,?1968.
[5]?Jaynes,?E.T.?Information?theory?and?statistical?mechanics.?Phys.?Rev.?1957,?106,?620-630.
[6]?Sang,?Y.F.,?D.?Wang,?J.C.?Wu,?Q.P.?Zhu,?L.?Wang.?The?relation?between?periods’?identification?and?noises?in?hydrologic?series?data.?Journal?of?Hydrology,?2009,?368?(1-4),?165-177.
[7]?Sang,?Y.F.,?D.?Wang,?J.C.?Wu,?Q.P.?Zhu,?L.?Wang.?Entropy-Based?Wavelet?De-noising?Method?for?Time?Series?Analysis.?Entropy,?2009,?11(?4),?1123-1147.
[8]?Huang,?N.E.,?Z.?Shen,?S.R.?Long,?et?al.?The?empirical?mode?decomposition?method?and?the?Hilbert?spectrum?for?non-stationary?time?series?analysis.?Proc?Roy?Soc?Lond,?1998,?454A,?903-995.
[9]?Wu,?Z.H.,?N.E.?Huang.?Ensemble?empirical?mode?decomposition:?a?noise-assisted?data?analysis?method.?Center?for?Ocean-Land-Atmosphere?Studies?Technical?Report?#193,?2005.
[10]?Wu,?Z.,?Huang,?N.E.,?2004.?A?study?of?the?characteristics?of?white?noise?using?the?empirical?mode?decomposition?method.?Proc.?R.?Soc.?Lond.?Ser.?A—Math.?Phys.Eng.?Sci.?460?(2046),?1597–1611.
[11]Kayhan,?A.S.?Evolutionary?maximum?entropy?spectral?analysis?of?chirps?in?noise.?Signal?Processing,?1999,?78?(2),?151-157.
Claims (3)
1. method of discerning the Hydrological Time Series cycle is characterized in that may further comprise the steps:
1) reliability of the inspection Hydrological Time Series of analyzing at first, pass through selection rational curve-fitting method, frontier point disposal route and end condition then after, confirm concrete population mean empirical mode decomposition method, i.e. the EEMD method;
2) use determined EEMD method and sequence is decomposed sequence
X (t)Decomposition result be designated as:
(8)
Wherein,
NThe number of the intrinsic mode function (IMFs) that expression identifies,
C i Expression the
iIndividual IMF,
R N Be last residual components, general corresponding the trend of sequence;
3) utilize the energy dispersal function of white noise, identify the determinacy intrinsic mode function among all IMFs, i.e. MIMFs;
4), use entropy spectral analysis method recognition cycle, i.e. the MESA method for each MIMFs;
5) the cycle recognition result of last comprehensive each MIMFs obtains cycle of the Hydrological Time Series of analyzing.
2. the method in identification Hydrological Time Series cycle according to claim 1 is characterized in that said step 2) EEMD method process that sequence is decomposed is:
Initialization:
i=1, and definition
r 0 =
X (t)
For
r 0 , discern all Local Extremum, comprise maximum value and minimal value, utilize cubic spline curve approximating method respectively match local maximum point and minimum point then, and as on cover line and under cover line;
Contrast is also found the solution the average curve that covers line up and down
m (j=1)
Through finding the solution sequence
r 0 With
m (j=1) Difference, obtain first sequence
h (j=1)
Will
h (j=1) As
r 0 Repeating step (2)-(4) then, constantly promptly
j=
j+ 1 is satisfying the requirement that meets under the certain criterion about horizontal ordinate symmetry until covering line up and down, last
h (j) The result is designated as
C i
Again definition
r 0 =
X (t)-
C i And
i=
i+ 1, repeating step (1)-(5) then, when
i=
NAnd residual components
R N Become a monotonic quantity, when only comprising inner extreme point and can not discern any IMF again, " screening " process finishes.
3. the method in identification Hydrological Time Series cycle according to claim 1 and 2 is characterized in that the process of step 4) is:
Order
XExpression waits to estimate the hydrology sequence of frequency spectrum, and the relational expression of hydrology sequence spectrum and entropy is:
Wherein,
f N Expression Nyquist frequency,
S (f)The expression frequency
fThe spectrum value at place,
E d Then represent entropy density;
For the Hydrological Time Series of appointment, formula (1) right-hand member first is a constant, and solution procedure only need guarantee that the integral maximization of second portion gets final product, so formula (1) can be reduced to:
Maximization:
(2)
Constraints:
? (3)
Wherein,
mThe maximum time lag of expression appointment,
i=(1)
1/2,
r x (k)The expression sequence
X kThe rank coefficient of autocorrelation;
Likewise, if wait to estimate frequency spectrum only with known exponent number on autocorrelation performance relevant, must satisfy the differentiate result of formula (4):
Following formula shows function
1/S (f)The Fourier transformation results in time lag
K=mThe place is blocked, and can obtain formula (5) then:
Maximum time lag or filter length do
mThe time, can obtain formula (6) through finding the solution entropy maximization:
In the formula,
P (m+1)Expression is to the energy value of back prediction error, γ
x (j)The filter coefficient that expression is used to forecast,
γ x (j)With
P (m+1)Then estimate to find the solution frequency spectrum through recursive algorithm
S (f)Estimate to obtain by formula (7):
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| CN104765979A (en) * | 2015-04-28 | 2015-07-08 | 南京信息工程大学 | Sea clutter denoising method based on integrated experience mode decomposition |
| CN105069309A (en) * | 2015-08-21 | 2015-11-18 | 中国科学院地理科学与资源研究所 | Method for identifying hydrologic time sequence nonlinear trend |
| CN105205217A (en) * | 2015-08-25 | 2015-12-30 | 中国科学院地理科学与资源研究所 | Method for judging hydrologic time series non-stationarity |
| CN110850162A (en) * | 2019-11-22 | 2020-02-28 | 西南交通大学 | Frequency estimation method of three-phase power system based on error correlation entropy |
-
2012
- 2012-02-27 CN CN201210045747XA patent/CN102622517A/en active Pending
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104765979A (en) * | 2015-04-28 | 2015-07-08 | 南京信息工程大学 | Sea clutter denoising method based on integrated experience mode decomposition |
| CN104765979B (en) * | 2015-04-28 | 2018-04-24 | 南京信息工程大学 | A kind of sea clutter denoising method based on integrated empirical mode decomposition |
| CN105069309A (en) * | 2015-08-21 | 2015-11-18 | 中国科学院地理科学与资源研究所 | Method for identifying hydrologic time sequence nonlinear trend |
| CN105205217A (en) * | 2015-08-25 | 2015-12-30 | 中国科学院地理科学与资源研究所 | Method for judging hydrologic time series non-stationarity |
| CN105205217B (en) * | 2015-08-25 | 2018-04-03 | 中国科学院地理科学与资源研究所 | A kind of method for differentiating that Hydrological Time Series are non-stationary |
| CN110850162A (en) * | 2019-11-22 | 2020-02-28 | 西南交通大学 | Frequency estimation method of three-phase power system based on error correlation entropy |
| CN110850162B (en) * | 2019-11-22 | 2020-09-29 | 西南交通大学 | Frequency estimation method of three-phase power system based on error correlation entropy |
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